Tag Archives: Mandelbrot

A Good Latitude

To start the last week of March Mathness, because it’s a Monday, I’m going to go easy on y’all with some light, easy topics. (Maybe I can lull you into paying attention for the major topic of the month: matrix rotation.)

It has occurred to me that, if I’m talking about math in March, I absolutely must mention one of my all-time favorite mathematical objects, the Mandelbrot. I’ll try to get to that today, but the main topic is a simple something that I ran into while working on my 3D model of the big island of Hawaii.

The question was: How many miles are there per degree of latitude?

Continue reading

Math Games #1

Back at the start of March Mathness I promised the math would be “fun” (really!), but anyone would be forgiven for thinking the previous two posts about Special Relativity weren’t all that much “fun.” (I really enjoy stuff like that, so it’s fun for me, but there’s no question it’s not everyone’s cup of tea.)

Trying to reach for something a bit lighter and potentially more appealing as the promised “fun,” I present, for your dining and dancing pleasure, a trio of number games that anyone can play and which might just tug at the corners of your enjoyment.

We can start with 277777788888899 (and why it’s special).

Continue reading

Edge of the Knife

The universe may not be connected in the Dirk Gently sense (or perhaps it is, wouldn’t that be fun?), but I can’t help but be bemused by those occasional moments of synchronicity. Just striking coincidences — almost certainly — and just a product of one’s own mind connecting personal dots, but still.

When a moment of such synchronicity involves favorite TV shows, South Park, NCIS, and Doctor Who, plus the Mandelbrot Set, it covers a lot of bases and adds an extra special element of cosmic delight. (Not to mention all the options for the lead image! (Except not really. Gotta be the new The Doctor!))

Fundamentally, it’s all another riff on an old standard: Yin-Yang.

Continue reading

Chaotic Thoughts

Pierre-Simon Laplace

Tick-Tock, goes the clock…

Last time, in the Determined Thoughts post, I talked about physical determinism, which is the idea that the universe is a machine — like a clock — that is ticking off the minutes of existence. The famous French mathematician, Pierre-Simon Laplace (the “French Newton”), was the first (in 1814) to articulate the idea of causal determinism.

We now know that quantum mechanics makes it impossible to know both the position and motion of particles, so Laplace’s Demon isn’t possible at the sub-atomic level. (It might be possible at the classical or macro level — that’s an open question.) Sometimes the issue of chaos theory is proposed as a counter-argument to determinism, so I thought I’d cover what chaos theory is and how it might apply.

If you want to skip to the punchline, the answer is it doesn’t apply at all.

Continue reading